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    Largest Ideals in Leavitt Path Algebras
    (Springer Basel Ag, 2020) Cam, Vural; Gil Canto, Cristobal; Kanuni, Muge; Siles Molina, Mercedes
    We identify the largest ideals in Leavitt path algebras: the largest locally left/right artinian (which is the largest semisimple one), the largest locally left/right noetherian without minimal idempotents, the largest exchange, and the largest purely infinite. This last ideal is described as a direct sum of purely infinite simple pieces plus purely infinite non-simple and non-decomposable pieces. The invariance under ring isomorphisms of these ideals is also studied.
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    The singular ideal and the socle of incidence rings
    (Hacettepe Univ, Fac Sci, 2021) Kanuni, Muge; Ozkan, Ozkay
    Let R be a ring with identity and I(X, R) be the incidence ring of a locally finite partially ordered set X over R. In this paper, we compute the socle and the singular ideal of the incidence ring for some X in terms of the socle of R and the singular ideal of R, respectively.